New inequalities for strongly exponentially generalized functions with applications

The aim of this paper is to introduce a new class of functions called strongly exponentially generalized $(m,\nu_{1},\nu_{2},g_{1},g_{2})$.Some new integral inequalities of trapezium-type for strongly exponentially generalized $(m,\nu_{1},\nu_{2},g_{1},g_{2})$ functions with modulus $c$ via Riemann-Liouville fractional integral are established. Also, some new estimates with respect to trapezium-type integral inequalities for strongly exponentially generalized $(m,\nu_{1},\nu_{2},g_{1},g_{2})$ functions with modulus $c$ via general fractional integrals are obtained. We show that the strongly exponentially generalized $(m,\nu_{1},\nu_{2},g_{1},g_{2})$ functions with modulus $c$ includes several other classes of functions. At the end, some new error estimates for trapezoidal quadrature formula are provided as well. This results may stimulate further research in different areas of pure and applied sciences.